Tony Mowbray's side have enjoyed an excellent start to the season, having picked up three wins and a draw from their opening four Championship games of the season.
They continued their impressive form this evening as first-half goals from Barry Robson and Seb Hines secured victory at London Road.
Both sides have enjoyed an excellent start to the season, with Middlesbrough occupying third in the second tier while Peterborough sit sixth.
Boro, clearly brimming with confidence on the back of their sensational opening to the campaign, flew out of the blocks and took an early lead.
With the hosts looking to stamp their authority on the game, a brilliant counter-attack ended with Joe Bennett freeing Robson, who slotted home.
Posh, though, were undeterred and continued to press forward with George Boyd seeing his curling effort saved by Danny Coyne.
But Darren Ferguson's men were proving no match for their rampant visitors, who added a second goal midway through the opening period.
Tony McMahon was the orchestrator, sending in a delicious corner which Hines was on hand to nod past Paul Jones.
Mowbray's side almost found themselves further ahead on the stroke of half-time but Jones reacted brilliantly to turn McMahon's effort onto the crossbar.
Clearly spurred on by Ferguson's half-time team talk, Peterborough came out strongly in the second period.
But Coyne was in a defiant mood for the visitors, first keeping out a fizzing Boyd effort before twice denying the impressive Lee Frecklington.
Posh continued to huff and puff but as the game wore on, chances became increasingly scarce and Mowbray's men saw the game out to secure their place in the third-round draw.